volume | PIER Journals

Abstract

In this paper, we propose a brief and general process to compute the eigenvalue of arbitrary waveguides using meshless method based on radial basis functions (MLM-RBF) interpolation. The main idea is that RBF basis functions are used in a point matching method to solve the Helmholtz equation only in Cartesian system. Two kinds of boundary conditions of waveguide problems are also anlyzed. To verify the e±ciency and accuracy of the present method, three typical waveguide problems are analyzed. It is found that the results of various waveguides can be accurately determined by MLM-RBF.

1. Arlett, P. L., A. K. Bahrani, and O. C. Zienkiewicz, "Application of finite element to the solution of Helmholtzs equation," Proc. IEE., Vol. 115, No. 12, 1762-1766, 1968. Google Scholar

2. Chang, H. W., Y. H. Wu, S. M. Lu, W. C. Cheng, and M. H. Sheng, "Field analysis of dielectric waveguide devices based on coupled transverse-mode integral equation --- Numerical investigation," Progress In Electromagnetics Research, Vol. 97, 159-176, 2009.
doi:10.2528/PIER09091402 Google Scholar

3. Khalaj-Amirhosseini, M., "Analysis of longitudinally inhomogeneous waveguides using the method of moments," Progress In Electromagnetics Research, Vol. 74, 57-67, 2007.
doi:10.2528/PIER07042101 Google Scholar

4. Lavranos, C. S. and G. A. Kyriacou, "Eigenvalue analysis of curved open waveguides using a finite difference frequency domain method employing orthogonal curvilinear coordinates," PIERS Online, Vol. 1, No. 3, 271-275, 2005.
doi:10.2529/PIERS041210160317 Google Scholar

5. Seydou, F., T. Seppanen, and O. M. Ramahi, "Computation of the Helmholtz eigenvalues in a class of chaotic cavities using the multipole expansion technique," IEEE Transactions on Antennas and Propagation, Vol. 57, No. 4, 1169-1177, 2009.
doi:10.1109/TAP.2009.2015801 Google Scholar

6. Reutskiy, S. Y., "The methods of external excitation for analysis of arbitrarily-shaped hollow conducting waveguides," Progress In Electromagnetics Research,, Vol. 82, 203-226, 2008.
doi:10.2528/PIER08022701 Google Scholar

7. Miao, Y., Y. Wang, and Y. H. Wang, "A meshless hybrid boundary-node method for Helmholtz problems," Eng. Anal. Boundary Elem., Vol. 33, No. 2, 120-127, 2009.
doi:10.1016/j.enganabound.2008.05.009 Google Scholar

8. Hon, Y. C. and W. Chen, "Boudary knot method for 2D and 3D helmholtz and convection-diffusion problems under complicated geometry," Int. J. Numer. Methods Eng., Vol. 56, No. 13, 1931-1948, 2003.
doi:10.1002/nme.642 Google Scholar

9. Christina, W. and O. Von Estorff, "Dispersion analysis of the meshfree radial point interpolation method for the Helmholtz equation," Int. J. Numer. Methods Eng., Vol. 77, No. 12, 1670-1689, 2009.
doi:10.1002/nme.2463 Google Scholar

10. Shu, C., W. X. Wu, and C. M. Wang, "Analysis of metallic waveguides by using least square-based finite difference method," Comput. Mater. Continua., Vol. 2, No. 3, 189-200, 2005. Google Scholar

11. Ooi, B. L. and G. Zhao, "Element-free method for the analysis of partially-filled dielectric waveguides," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 2, 189-198, 2007.
doi:10.1163/156939307779378772 Google Scholar

12. Liu, X. F., B. Z. Wang, and S. J. Lai, "Element-free Galerkin method for transient electromagnetic field simulation," Microw. Opt. Techn. Let., Vol. 50, No. 1, 134-138, 2008.
doi:10.1002/mop.23017 Google Scholar

13. Kansa, E. J., "Multiqudrics --- A scattered data approximation scheme with applications to computational fluid-dynamics --- I: Surface approximations and partial derivatives," Computer Math. Applic., Vol. 9, No. 8--9, 127-145, 1992. Google Scholar

14. Zhao, G., B. L. Ooi, Y. J. Fan, Y. Q. Zhang, I. Ang, and Y. Gao, "Application of conformal meshless RBF coupled with coordinate transformation for arbitrary waveguide analysis," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 1, 3-14, 2007.
doi:10.1163/156939307779391731 Google Scholar

15. Jiang, P. L., S. Q. Li, and C. H. Chuan, "Analysis of elliptical waveguides by a meshless collocation method with the Wendland radial basis funcitons," Microwave Opt. Technol. Lett., Vol. 32, No. 2, 162-165, 2002.
doi:10.1002/mop.10119 Google Scholar

16. Yu, J. H. and H. Q. Zhang, "Solving waveguide eigenvalue problem by using radial basis function method," World Autom. Congr. WAC, Vol. 1, 1-5, 2008. Google Scholar

17. Lai, S. J., B. Z. Wang, and Y. Duan, "Application of the RBF-based meshless method to solve 2-D time domain maxwells equations," Int. Conf. Microw. Millimeter Wave Technol. Proc. ICMMT, Vol. 2, 749-751, 2008. Google Scholar

18. Lai, S. J., B. Z. Wang, and Y. Duan, "Meshless radial basis function method for transient electromagnetic computations," IEEE Trans. Magn., Vol. 44, No. 10, 2288-2295, 2008.
doi:10.1109/TMAG.2008.2001796 Google Scholar

19. Fornberg, B., T. A. Driscoll, G. Wright, and R. Charles, "Observations on the behavior of radial basis function approximation near boundaries ," Comput. Math. Appl., Vol. 43, No. 3, 473-490, 2002.
doi:10.1016/S0898-1221(01)00299-1 Google Scholar

20. Wu, Z. M., "Compactly supported positive definite radial functions," Adv. Comput. Math., Vol. 4, 283-292, 1995.
doi:10.1007/BF03177517 Google Scholar

21. Zhang, K. Q. and D. J. Li, Electromagnetic Theory for Microwaves and Optoelectronics, No. 4, Springer Press, 2008.

22. Zhang, S. J. and Y. C. Shen, "Eigenmode sequence for an elliptical waveguide with arbitrary ellipticity," IEEE Trans. MTT., Vol. 43, No. 1, 221-224, 1995. Google Scholar

23. Lin, W. G., Microwave Theory and Techniques, 158-162, Science Press, 1979 (in Chinese).

Dr. Sheng-Jian Lai

Professor Bing-Zhong Wang

Dr. Yong Duan